#!/usr/bin/env python3
"""
Wolfram Alpha Mathematical Verification — SilverSight
Verifies all core mathematical claims of the project.
"""
import urllib.request, urllib.parse, json, sys, os, hashlib

APPID = "HYJE3R3R63"

QUERIES = {
    # ── Q16_16 fixed-point arithmetic ─────────────────────────────
    "q16_scale_factor": "65536",
    "q16_mul_identity": "simplify (a * b / 65536) when a = 65536",
    "q16_saturation_bounds": "range of int32 signed integer",

    # ── Rossby/Kelvin wave correspondence ─────────────────────────
    "rossby_dispersion": "omega = -beta * k / (k^2 + l^2) Rossby wave dispersion",
    "kelvin_wave_nondispersive": "omega = k * sqrt(g * H) Kelvin wave",
    "rossby_deformation_radius": "L_D = sqrt(g * H) / f Rossby deformation radius",

    # ── Golden ratio / corkscrew ──────────────────────────────────
    "golden_ratio_conjugate": "solve x^2 - x - 1 = 0",
    "corkscrew_angle": "2 * pi / ((1 + sqrt(5)) / 2)^2",

    # ── Fisher information metric ─────────────────────────────────
    "fisher_metric_simplex": "arccos(sum sqrt(p_i * q_i))",
    "fisher_distance": "2 * arccos(sqrt(p * q)) Fisher distance",
    "cauchy_schwarz_fisher": "sum sqrt(p_i * q_i) <= 1 for probability distributions",

    # ── Eigensolid convergence ────────────────────────────────────
    "pair_averaging_idempotent": "simplify ((a+b)/2 + (c+d)/2) / 2",
    "pair_averaging_contractive": "prove |(a+b)/2 - (c+d)/2| < |a-c| + |b-d|",
    "chaos_game_contraction": "prove (1-eps)^k < 2^(-k) for 0 < eps < 1",

    # ── NUVMAP projection ─────────────────────────────────────────
    "nuvmap_eigenmass": "limit lambda * v * S * L / (R + epsilon) as R -> 0",
    "bekenstein_bound": "A / (4 * L_p^2) Bekenstein bound",
    "eigenvalue_power_iteration": "Rayleigh quotient convergence power iteration",

    # ── Sidon sets ────────────────────────────────────────────────
    "sidon_condition": "powers of 2 pairwise distinct sums",
    "sidon_slack_128": "128 - 2^7 =",
    "binary_sidon_max_sum": "max sum of distinct powers of 2 from 1,2,4,...,128",
}

def query_wolfram(query):
    encoded = urllib.parse.quote_plus(query)
    url = f"http://api.wolframalpha.com/v2/query?appid={APPID}&input={encoded}&format=plaintext&output=JSON"
    try:
        req = urllib.request.Request(url, headers={'User-Agent': 'SilverSight/1.0'})
        with urllib.request.urlopen(req, timeout=15) as resp:
            return json.loads(resp.read().decode('utf-8'))
    except Exception as e:
        return {"error": str(e)}

def extract_result(res):
    if "error" in res:
        return f"[ERROR: {res['error']}]"
    if "queryresult" not in res:
        return "[no queryresult]"
    qr = res["queryresult"]
    for pod in qr.get("pods", []):
        for subpod in pod.get("subpods", []):
            if "plaintext" in subpod and subpod["plaintext"]:
                return subpod["plaintext"]
    return "[no plaintext result]"

def main():
    results = {}
    for name, query in QUERIES.items():
        print(f"  {name}...", end=" ", flush=True)
        resp = query_wolfram(query)
        text = extract_result(resp)
        results[name] = {"query": query, "result": text}
        print(text[:80] if text else "(empty)")

    # Build receipt
    receipt = {
        "schema": "wolfram_verification_v2",
        "generated_at": __import__('datetime').datetime.utcnow().isoformat(),
        "n_queries": len(QUERIES),
        "queries": results,
        "claim_boundary": "wolfram-alpha-algebraic-verification-only",
    }
    payload = json.dumps(results, sort_keys=True).encode()
    receipt["receipt_hash"] = hashlib.sha256(payload).hexdigest()[:16]

    path = os.path.expanduser("~/SilverSight/signatures/wolfram_verification_receipt.json")
    os.makedirs(os.path.dirname(path), exist_ok=True)
    with open(path, "w") as f:
        json.dump(receipt, f, indent=2)
    print(f"\nReceipt: {path}")

if __name__ == "__main__":
    main()